The theory of the determination of wages in a free market is simply a special case of the general theory of value. Wages are the price of labour.
I think of the described dynamics as a fluid negotiation. I don't think these specific interactions can happen to the black or brown body without the white body. And there are ways in which, if you say, "Oh, this happened to me," then the white body can say, "Well, it happened to her and it has nothing to do with me. " But if it says "you," that you is an apparent part of the encounter.